Abstract
A general framework for studying the transitivity of reciprocal relations is presented. The key feature is the cyclic evaluation of transitivity: triangles (i.e. any three points) are visited in a cyclic manner. An upper bound function acting upon the ordered weights encountered provides an upper bound for the ‘sum minus 1’ of these weights. Commutative quasi-copulas allow to translate a general definition of fuzzy transitivity (when applied to reciprocal relations) elegantly into the framework of cycle-transitivity. Similarly, a general notion of stochastic transitivity corresponds to a particular class of upper bound functions. Ample attention is given to self-dual upper bound functions.
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Baets, B.D., Meyer, H.D. & Schuymer, B.D. Cyclic Evaluation of Transitivity of Reciprocal Relations. Soc Choice Welfare 26, 217–238 (2006). https://doi.org/10.1007/s00355-006-0093-3
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DOI: https://doi.org/10.1007/s00355-006-0093-3